The invention relates to a fuel injection system of the type described herein and finally claimed. A fuel injection system is already known in which a spring reservoir is provided in the fuel supply line for the purpose of preventing vapor bubbles after the internal combustion engine is turned off and to compensate for volumetric changes when the engine temperature is dropping after the engine is turned off or volumetric changes caused by leakage of fuel out of the system. However, in such a system there is the disadvantage that the reservoir volume cannot be made to be as large as desired, so that when the fuel injection system is not in operation the movable reservoir element contacts its end stop after a relatively short time, and further vapor bubble information can no longer be prevented and a further compensation for a lessening in fuel volume is no longer possible. This often causes misfiring, in the event of restarting of the internal combustion engine, until such time as the system is again completely filled with fuel.